We conclude this work by defining a hermitian conjugation relation for the quasi-primary multiplet fields, in the same spirit as the BPZ conjugation [1]} in 2D relativistic CFTs. The \(1+1\) D Carrollian conformal inversion transformation is at the core of this construction. By extending the `stereographic projection of the circle \((\theta )\)  onto the line \((x)\) ' to the following Carrollian conformal transformation:
\(\theta \rightarrow x=-\cot \frac{\theta }{2}\hspace{7.11317pt};\hspace{7.11317pt}\tau \rightarrow t=\frac{\tau }{2}\csc ^2\frac{\theta }{2}\) 
